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Properties

Label 19.9
Level 19
Weight 9
Dimension 111
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 270
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(270\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(19))\).

Total New Old
Modular forms 129 129 0
Cusp forms 111 111 0
Eisenstein series 18 18 0

Trace form

\( 111 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} + O(q^{10}) \) \( 111 q - 9 q^{2} - 9 q^{3} - 9 q^{4} - 9 q^{5} - 9 q^{6} - 9 q^{7} - 9 q^{8} - 9 q^{9} - 9 q^{10} - 9 q^{11} - 124425 q^{12} + 20211 q^{13} + 214263 q^{14} + 10197 q^{15} - 548361 q^{16} - 151776 q^{17} + 502710 q^{19} + 1285614 q^{20} + 430344 q^{21} - 556425 q^{22} - 583074 q^{23} - 2612745 q^{24} - 157383 q^{25} + 2087415 q^{26} + 4849875 q^{27} - 7671774 q^{28} - 1422153 q^{29} + 8144820 q^{30} + 3498759 q^{31} + 4624416 q^{32} - 3477609 q^{33} - 9311094 q^{34} - 9057321 q^{35} - 15646815 q^{36} + 12932316 q^{38} + 19452510 q^{39} + 24702066 q^{40} + 4723479 q^{41} - 1247859 q^{42} - 2609142 q^{43} - 42236028 q^{44} - 66337200 q^{45} - 30318354 q^{46} + 18155142 q^{47} + 126808218 q^{48} + 43982490 q^{49} + 30782124 q^{50} - 55636380 q^{51} - 54269961 q^{52} - 39714525 q^{53} - 55921248 q^{54} - 22880853 q^{55} + 31888026 q^{57} + 46900206 q^{58} + 72383076 q^{59} + 270839340 q^{60} - 26759469 q^{61} - 147481812 q^{62} - 117924597 q^{63} - 93267249 q^{64} + 2267586 q^{65} + 24824799 q^{66} + 137971524 q^{67} + 119963016 q^{68} + 54287784 q^{69} - 24607773 q^{70} + 2206350 q^{71} - 534275244 q^{72} - 290081796 q^{73} - 112791393 q^{74} + 152873901 q^{76} + 418844367 q^{77} + 249834177 q^{78} + 221930205 q^{79} - 50027697 q^{80} + 125816787 q^{81} + 88500186 q^{82} + 57964212 q^{83} + 143496459 q^{84} - 293049765 q^{85} - 333573210 q^{86} - 399729969 q^{87} - 412023537 q^{88} + 54872550 q^{89} + 60928776 q^{90} + 380290515 q^{91} + 73124226 q^{92} - 355579569 q^{93} + 82012896 q^{95} - 155599434 q^{96} - 303877602 q^{97} - 107101584 q^{98} + 677736423 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(19))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
19.9.b \(\chi_{19}(18, \cdot)\) 19.9.b.a 1 1
19.9.b.b 12
19.9.d \(\chi_{19}(8, \cdot)\) 19.9.d.a 26 2
19.9.f \(\chi_{19}(2, \cdot)\) 19.9.f.a 72 6